Essentials of Statistics (5th Edition)
5th Edition
ISBN: 9780321924599
Author: Mario F. Triola
Publisher: PEARSON
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Chapter 7.2, Problem 12BSC
To determine
To express: The confidence interval for Blue M&Ms in the form of
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In Gallup's Annual Consumption Habits Poll, telephone interviews were conducted for a random sample of 1014 adults aged 18 and over. One of the questions was "How many cups of coffee, if any, do you drink on an average day?" The following table shows the results obtained (Gallup website, August 6, 2012).
Excel File: data05-23.xls
Number of Cups
per Day
Number of
Responses
0
365
264
193
2
3
4 or more
91
101
Define a random variable x = number of cups of coffee consumed on an average day. Let x = 4 represent four or more cups.
Round your answers to four decimal places.
a. Develop a probability distribution for x.
x
0
1
2
3
f(x)
b. Compute the expected value of x.
cups of coffee
c. Compute the variance of x.
cups of coffee squared
d. Suppose we are only interested in adults that drink at least one cup of coffee on an average day. For this group, let y = the number of cups of coffee consumed on an average day.
Compute the expected value of y.
Compare it to the expected value of x.
The…
A technician services mailing machines at companies in the Phoenix area. Depending on the type of malfunction, the service call can take 1, 2, 3, or 4 hours. The different types of malfunctions occur at about the same frequency.
Develop a probability distribution for the duration of a service call.
Duration of Call
x
f(x)
1
2
3
4
Which of the following probability distribution graphs accurately represents the data set?
Consider the required conditions for a discrete probability function, shown below.Does this probability distribution satisfy equation (5.1)?Does this probability distribution satisfy equation (5.2)?
What is the probability a service call will take three hours?
A service call has just come in, but the type of malfunction is unknown. It is 3:00 P.M. and service technicians usually get off at 5:00 P.M. What is the probability the service technician will have to work overtime to fix the machine today?
A psychologist determined that the number of sessions required to obtain the trust of a new patient is either 1, 2, or 3. Let x be a random variable indicating the number of sessions required to gain the patient's trust. The following probability function has been proposed.
x
f(x)
for x = 1, 2, or 3
a. Consider the required conditions for a discrete probability function, shown below.
f(x) ≥0
Σf(x) = 1
(5.1)
(5.2)
Does this probability distribution satisfy equation (5.1)?
Select
Does this probability distribution satisfy equation (5.2)?
Select
b. What is the probability that it takes exactly 2 sessions to gain the patient's trust (to 3 decimals)?
c. What is the probability that it takes at least 2 sessions to gain the patient's trust (to 3 decimals)?
Chapter 7 Solutions
Essentials of Statistics (5th Edition)
Ch. 7.2 - 2. Margin of Error For the poll described in...Ch. 7.2 - Statistical Literacy and Critical Thinking
1. Poll...Ch. 7.2 - 3. Notation For the poll described in Exercise 1,...Ch. 7.2 - 4. Confidence Levels Given specific sample data,...Ch. 7.2 - Finding Critical Values. In Exercises 5-8, find...Ch. 7.2 - Prob. 6BSCCh. 7.2 - Finding Critical Values. In Exercises 5-8, find...Ch. 7.2 - Finding Critical Values. In Exercises 5-8, find...Ch. 7.2 - Formats of Confidence Intervals. In Exercises...Ch. 7.2 - Formats of Confidence Intervals. In Exercises...
Ch. 7.2 - Formats of Confidence Intervals. In Exercises...Ch. 7.2 - Formats of Confidence Intervals. In Exercises...Ch. 7.2 - Constructing and Interpreting Confidence...Ch. 7.2 - Constructing and Interpreting Confidence...Ch. 7.2 - Constructing and Interpreting Confidence...Ch. 7.2 - Constructing and Interpreting Confidence...Ch. 7.2 - 17. Gender Selection The Genetics and IVF...Ch. 7.2 - 18. Gender Selection The Genetics and IVF...Ch. 7.2 - Prob. 19BSCCh. 7.2 - 20. Mendelian Genetics When Mendel conducted his...Ch. 7.2 - 21. Online Books A Consumer Reports Research...Ch. 7.2 - 22. Want Boss’s Job? In a USA Today survey, 20.8%...Ch. 7.2 - 23. Job Interviews In a Harris poll of 514 human...Ch. 7.2 - 24. Job Interviews In a Harris poll of 514 human...Ch. 7.2 - Prob. 25BSCCh. 7.2 - Prob. 26BSCCh. 7.2 - Prob. 27BSCCh. 7.2 - Prob. 28BSCCh. 7.2 - Determining Sample Size. In Exercises 29-36, use...Ch. 7.2 - Determining Sample Size. In Exercises 29-36, use...Ch. 7.2 - Determining Sample Size. In Exercises 29-36, use...Ch. 7.2 - Determining Sample Size. In Exercises 29-36, use...Ch. 7.2 - Prob. 33BSCCh. 7.2 - Determining Sample Size. In Exercises 29-36, use...Ch. 7.2 - Determining Sample Size. In Exercises 29-36, use...Ch. 7.2 - Determining Sample Size. In Exercises 29-36, use...Ch. 7.2 - Using Appendix B Data Sets. In Exercises 37 and...Ch. 7.2 - Using Appendix B Data Sets. In Exercises 37 and...Ch. 7.2 - 39. Finite Population Correction Factor For...Ch. 7.2 - 40. Confidence Interval from Small Sample Special...Ch. 7.2 - Prob. 41BBCh. 7.2 - Prob. 42BBCh. 7.2 - Prob. 43BBCh. 7.3 - In Exercises 1-3, refer to the accompanying screen...Ch. 7.3 - Statistical Literacy and Critical Thinking
In...Ch. 7.3 - In Exercises 1-3, refer to the accompanying screen...Ch. 7.3 - 4. Normality Requirement What does it mean when we...Ch. 7.3 - Using Correct Distribution. In Exercises 5-8,...Ch. 7.3 - Using Correct Distribution. In Exercises 5-8,...Ch. 7.3 - Using Correct Distribution. In Exercises 5-8,...Ch. 7.3 - Using Correct Distribution. In Exercises 5-8,...Ch. 7.3 - Confidence Intervals. In Exercises 9-24, construct...Ch. 7.3 - Confidence Intervals. In Exercises 9-24, construct...Ch. 7.3 - Confidence Intervals. In Exercises 9-24, construct...Ch. 7.3 - Confidence Intervals. In Exercises 9-24, construct...Ch. 7.3 - Prob. 13BSCCh. 7.3 - Prob. 14BSCCh. 7.3 - Prob. 15BSCCh. 7.3 - Prob. 16BSCCh. 7.3 - Prob. 17BSCCh. 7.3 - Prob. 18BSCCh. 7.3 - Prob. 19BSCCh. 7.3 - Prob. 20BSCCh. 7.3 - Prob. 21BSCCh. 7.3 - Prob. 22BSCCh. 7.3 - Confidence Intervals. In Exercises 9-24, construct...Ch. 7.3 - Prob. 24BSCCh. 7.3 - Prob. 25BSCCh. 7.3 - Prob. 26BSCCh. 7.3 - Prob. 27BSCCh. 7.3 - Prob. 28BSCCh. 7.3 - Prob. 29BSCCh. 7.3 - Prob. 30BSCCh. 7.3 - Prob. 31BSCCh. 7.3 - Prob. 32BSCCh. 7.3 - Prob. 33BSCCh. 7.3 - Prob. 34BSCCh. 7.3 - Prob. 35BBCh. 7.3 - Prob. 36BBCh. 7.3 - Prob. 37BBCh. 7.3 - Prob. 38BBCh. 7.3 - Prob. 39BBCh. 7.3 - Prob. 40BBCh. 7.3 - Prob. 41BBCh. 7.4 - 1. LDL Cholesterol Using the 40 LDL cholesterol...Ch. 7.4 - Prob. 2BSCCh. 7.4 - Prob. 3BSCCh. 7.4 - Prob. 4BSCCh. 7.4 - Prob. 5BSCCh. 7.4 - Prob. 6BSCCh. 7.4 - Prob. 7BSCCh. 7.4 - Prob. 8BSCCh. 7.4 - Prob. 9BSCCh. 7.4 - Prob. 10BSCCh. 7.4 - Prob. 11BSCCh. 7.4 - Finding Confidence Intervals. In Exercises 9-16,...Ch. 7.4 - Prob. 13BSCCh. 7.4 - Prob. 14BSCCh. 7.4 - Prob. 15BSCCh. 7.4 - Prob. 16BSCCh. 7.4 - Prob. 17BSCCh. 7.4 - Prob. 18BSCCh. 7.4 - Determining Sample Size. In Exercises 19-22,...Ch. 7.4 - Prob. 20BSCCh. 7.4 - Prob. 21BSCCh. 7.4 - Prob. 22BSCCh. 7.4 - Prob. 23BBCh. 7 - Prob. 1CQQCh. 7 - Prob. 2CQQCh. 7 - Prob. 3CQQCh. 7 - Prob. 4CQQCh. 7 - Prob. 5CQQCh. 7 - Prob. 6CQQCh. 7 - Prob. 7CQQCh. 7 - Prob. 8CQQCh. 7 - Prob. 9CQQCh. 7 - Prob. 10CQQCh. 7 - 1. Overpaid In a Gallup poll of 557 randomly...Ch. 7 - Prob. 2RECh. 7 - Prob. 3RECh. 7 - Prob. 4RECh. 7 - Prob. 5RECh. 7 - Prob. 6RECh. 7 - Prob. 7RECh. 7 - Prob. 8RECh. 7 - Prob. 9RECh. 7 - Prob. 10RECh. 7 - Prob. 1CRECh. 7 - Prob. 2CRECh. 7 - Prob. 3CRECh. 7 - Prob. 4CRECh. 7 - Prob. 5CRECh. 7 - Prob. 6CRECh. 7 - 7. Purell Survey In a survey of 1003 people, 59%...Ch. 7 - Prob. 8CRECh. 7 - Prob. 9CRECh. 7 - Prob. 10CRECh. 7 - Prob. 1FDDCh. 7 - Prob. 2FDDCh. 7 - Prob. 3FDDCh. 7 - Prob. 5FDDCh. 7 - Prob. 6FDD
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- A technician services mailing machines at companies in the Phoenix area. Depending on the type of malfunction, the service call can take 1, 2, 3, or 4 hours. The different types of malfunctions occur at about the same frequency. Develop a probability distribution for the duration of a service call. Which of the following probability distribution graphs accurately represents the data set? Consider the required conditions for a discrete probability function, shown below.Does this probability distribution satisfy equation (5.1)?Does this probability distribution satisfy equation (5.2)? What is the probability a service call will take three hours? A service call has just come in, but the type of malfunction is unknown. It is 3:00 P.M. and service technicians usually get off at 5:00 P.M. What is the probability the service technician will have to work overtime to fix the machine today?arrow_forwardWest Virginia has one of the highest divorce rates in the nation, with an annual rate of approximately 5 divorces per 1000 people (Centers for Disease Control and Prevention website, January 12, 2012). The Marital Counseling Center, Inc. (MCC) thinks that the high divorce rate in the state may require them to hire additional staff. Working with a consultant, the management of MCC has developed the following probability distribution for x = the number of new clients for marriage counseling for the next year. Excel File: data05-19.xls 10 20 f(x) .05 .10 11 30 40 50 60 .10 .20 .35 .20 a. Is this probability distribution valid? Yes Explain. greater than or equal to 0 f(x) Σf(x) equal to 1 b. What is the probability MCC will obtain more than 30 new clients (to 2 decimals)? c. What is the probability MCC will obtain fewer than 20 new clients (to 2 decimals)? d. Compute the expected value and variance of x. Expected value Variance clients per year squared clients per yeararrow_forwardReconsider the patient satisfaction data in Table 1. Fit a multiple regression model using both patient age and severity as the regressors. (a) Test for significance of regression. (b) Test for the individual contribution of the two regressors. Are both regressor variables needed in the model? (c) Has adding severity to the model improved the quality of the model fit? Explain your answer.arrow_forward
- The output voltage of a power supply is assumed to be normally distributed. Sixteen observations taken at random on voltage are as follows: 10.35, 9.30, 10.00, 9.96, 11.65, 12.00, 11.25, 9.58, 11.54, 9.95, 10.28, 8.37, 10.44, 9.25, 9.38, and 10.85. (a) Test the hypothesis that the mean voltage equals 12 V against a two-sided alternative using a = 0.05. (b) Construct a 95% two-sided confidence interval on μ. (c) Test the hypothesis that σ² = 11 using α = 0.05. (d) Construct a 95% two-sided confidence interval on σ. (e) Construct a 95% upper confidence interval on σ. (f) Does the assumption of normality seem reasonable for the output voltage?arrow_forwardAnalyze the residuals from the regression model on the patient satisfaction data from Exercise 3. Comment on the adequacy of the regression model.arrow_forwardConsider the hypotheses: Hop=po H₁ppo where 2 is known. Derive a general expression for determining the sample size for detecting a true mean of 1μo with probability 1-ẞ if the type I error is a.arrow_forward
- Suppose we wish to test the hypotheses: Họ : | = 15 H₁: 15 where we know that o² = 9.0. If the true mean is really 20, what sample size must be used to ensure that the probability of type II error is no greater than 0.10? Assume that a = 0.05.arrow_forwardTable 1 contains the data from a patient satisfaction survey for a group of 25 randomly selected patients at a hospital. In addition to satisfaction, data were collected on patient age and an index that measured the severity of illness. (a) Fit a linear regression model relating satisfaction to patient age. (b) Test for significance of regression. (c) What portion of the total variability is accounted for by the regressor variable age? Table 1: Patient Satisfaction Data Severity Observation Age (21) (x2) Satisfaction (y) 1 55 50 2 46 24 3 30 46 4 35 48 5 59 58 6 61 60 7 74 65 8 38 42 9 27 42 10 51 50 11 53 38 12 41 30 13 37 31 88 14 24 34 15 42 30 16 50 48 17 58 61 18 60 71 19 62 62 20 68 38 21 70 41 22 79 66 23 63 31 24 39 42 25 49 40 BE225222222222222222 68 77 96 80 43 44 26 88 75 57 56 88 102 88 70 43 46 56 59 26 83 75arrow_forward14 A survey is conducted to determine whether would prefer to work at home, if given the 20 office employees of a certain company chance. The overall results are shown in the first bar graph, and the results broken down by gender are presented in the second. a. Interpret the results of each graph. b. Discuss the added value in including gen- der in the second bar graph. (The second bar graph in this problem is called a side by side bar graph and is often used to show results broken down by two or more variables.) c. Compare the side by side bar graph with the two pie charts that you made for Question 6. Which of the two methods is best for comparing two groups, in your opinion? A Would you prefer to work at home? (n=20) 60 50 40 Percent 20 30 20 30 10 0 No Yes Prefer to work at home? (10 males, 10 females) 80 Percent 60 00 40 40 20- No Yes No Yes Female Malearrow_forward
- Frequency 12 Suppose that a random sample of 270 gradu- ating seniors are asked what their immediate priorities are, including whether buying a house is a priority. The results are shown in the following bar graph. a. The bar graph is misleading; explain why. b. Make a new bar graph that more fairly presents the results. Is Buying a House a Priority? 300 250 200 150 100 50 0 Yes No Undecidedarrow_forwardFrequency 11 A polling organization wants to find out what voters think of Issue X. It chooses a random sample of voters and asks them for their opinions of Issue X: yes, no, or no opinion. I organize the results in the following bar graph. a. Make a frequency table of these results (including the total number). brocb. Evaluate the bar graph as to whether it biz s b fairly represents the results. of beau no STORE TO OW! vd wob spind 550 540 500 vd 480 420 360 300 250 240 Yes No Undecided Opinion on Issue Xarrow_forwardPercent 13 A car dealer specializing in minivan sales saibe conducts a survey to find out more about who its customers are. One of the variables at the company measures is gender; the results of this part of the survey are shown in the following bar graph. pow a. Interpret these results. b. Explain whether you think the bar graph is a fair and accurate representation of this data. 70 Gender of Customers 60 50 40 30 20 10 0 Males Femalesarrow_forward
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